# oa.operator algebras – Projections in a type III factor

Any factor of type III can be described as the cross product of a type $$II_{infty}$$ von Neumann algebra $$N$$ by a certain one-parameter automorphism group $$G$$.

If $$p$$ is any projection the the factor of type III, can we construt $$p$$ by means of the projections in $$N$$?